Any which way the wind blows (physics brainteaser)

[Michael C]

Just a general comment to all participants in this thread, some of which I have shared other threads with: This forum has a very high percentage of bright, reasoned people as compared to many other forums I have participated in.

This speaks very well of skeptics IMO.

Thanks to all.

JB

And as an added bonus, we have Humber.

 

[rehn]

Well… The wording in my first message was not a good one, but I still think is was essentially correct. If the pilot has to fly a bit longer upwind (north in this case )at each revolution to stay in the thermal, it is the same as to say that the terminal appears to move upwind in relation to the ambient air mass.

About my flying experience ~25 years ago: I never had the opportunity to soare in terminals, it was ridge soaring only for me in my hang glider. But a few years ago I got a test lessen in a glider as a birth day gift from my sons. It was a 60 minutes flight on a day with good thermals. We where up at the cloud base at several occasions,
Now I only fly with the puter, my favorite is Spitfire on a flight simulator where “pilots” for all over the world are playing “Battle of Britain” etc…
Btw: Rhen is a river in Germany.
Rehn

 

[Clive]

Well… The wording in my first message was not a good one, but I still think is was essentially correct.

Actually, I think your wording was fine, and your answer was 100% correct. (It was very brief though, so perhaps it is easier to understand if the reader has some experience as a pilot.)

In any case, your solution has priority, and I relinquish any claim to the prize.

 

[Uncayimmy]

Can a pilot of an uninstrumented and unpowered soaring aircraft make any useful determination regarding which direction the wind is blowing at flight level *without* using clues seen outside the cockpit?

How do you fly in a circle without using clues outside of the cockpit?

 

[ThinAirDesigns]

Well… The wording in my first message was not a good one, but I still think is was essentially correct.

I agree, and that's why I credited you with being the first participant to provide a working solution.

If the pilot has to fly a bit longer upwind (north in this case )at each revolution to stay in the thermal, it is the same as to say that the terminal appears to move upwind in relation to the ambient air mass.

This is where I disagree with you but I certainly concede that it depends on the definition of the word "appears". I again argue that it only appears to move relative to the pilot/aircraft, and not the airmass -- if you smoked up the airmass one color and the thermal another, since they have the same horizontal velocity there would be no angle where they "appear" to move relative to each other.

Having said that, if I view only a vertical slice of a rotating, spirally adorned barber pole, it can "appear" as though the movement of the stripes is vertical rather than horizontal -- in similar context I can understand your point.

One thing I'm certain of ... you understand it and this is merely a difference in wording -- something that doesn't take away from that understanding.

JB

 

[ThinAirDesigns]

Just as an interesting aside, of people who have a bit of physics training, most are pretty fast to say "can't be determined". It's quickly considered to be the equal of the "can you tell if you're moving while in a box in space" problem.

Also, over time I have altered the wording slightly -- I used to ask if you could make this determination "without ground reference". This led to a battle with Spork for more than a decade now (we met online through this brainteaser) regarding the definition of the term "ground reference".

Spork maintains that without ground reference the thermal wouldn't tilt and thus using the 'tilt' information violated the rules of the original problem. I've changed the wording so as not to embarrass him further.

JB

 

[ThinAirDesigns]

How do you fly in a circle without using clues outside of the cockpit?

Nowhere does the problem state that you can't use outside clues to fly in a circle. For instance, using the horizon to set bank angle is perfectly legal -- I even later stipulated that I would allow an artificial horizon to be used if someone wished.

JB

 

[Clive]

How do you fly in a circle without using clues outside of the cockpit?

The OP clarified some of this later. He allowed for some basic instruments, and/or the ability to see the horizon so you could determine your angle of bank (for example).

Perhaps the better way to imagine this is to say you are flying on instruments alone and those instruments allow you to determine your speed relative to the air, aircraft orientation relative to the ground plus height above it, and you have a clock to determine how fast these values change also.

There's bit of question mark hanging over how realistic it would be to expect a pilot to maintain a "perfect orbit" at a fixed altitude with a very minimal set of instruments, but I think just a compass, altimeter and airspeed indicator (plus brain!) could be enough (in some theoretical sense at least) to solve this puzzle. That gives you direction, altitude, and airspeed directly. By observing the rate of change in those you can infer other details although this is also relying on your internal "clock" to some degree and understanding of aerodynamics. By observing how these things change as you orbit partially in and out of a thermal (or by determining what you need to do to descend or climb while also staying completely inside a thermal) you can determine the direction of the wind.

I should add that my memory of trying to maintain level flight in an orbit while also using a minimal set of instruments as described above (and possibly also trying to speak on the radio and read a map at the same time) is that I ended up in a screaming dive with my instructor yelling abuse at me!

 

[Uncayimmy]

Nowhere does the problem state that you can't use outside clues to fly in a circle. For instance, using the horizon to set bank angle is perfectly legal -- I even later stipulated that I would allow an artificial horizon to be used if someone wished.

As originally written it sounded like a relativity question. In effect it said, "Given a velocity of something (wind) relative to the ground, how can you determine this without referencing the ground."

That aside, you didn't answer my question. I don't fly, so how do you do it? If I can see the horizon, I can set my bank angle, keep it there, and I will go in a circle? How do I know when I have completed a circle without a reference point on the ground (a clue outside the cockpit)?

 

[ThinAirDesigns]

... you didn't answer my question. I don't fly, so how do you do it? If I can see the horizon, I can set my bank angle, keep it there, and I will go in a circle? How do I know when I have completed a circle without a reference point on the ground (a clue outside the cockpit)?

Once again, there is nothing in the problem that states you can't use clues outside the cockpit to fly the plane. If you wish to know when you've completed a circle, pick a cloud -- this will give you relative reference for the circle but no information related to steady wind direction.

JB

 

[ThinAirDesigns]

There's bit of question mark hanging over how realistic it would be to expect a pilot to maintain a "perfect orbit" at a fixed altitude with a very minimal set of instruments, but I think just a compass, altimeter and airspeed indicator (plus brain!) could be enough (in some theoretical sense at least) to solve this puzzle.

As someone with something around 3,000hrs in hang gliders, most of those with no instruments whatsoever, the brain alone is plenty instrument enough.

Now, soaring instruments integrate GPS and give wind direction aloft readily. Before those days on XC flights (261 miles is my longest in a hang glider) I used the described method every climb to monitor winds aloft. This knowledge allowed me to pick overall direction for best speed over the ground and thus maximize distance. Trying to use the ground as a reference, even when it's quite visible, is difficult if you are 15,000ft agl. This method can actually be surprisingly good.

It's really not only a theoretical problem ... it's a usefull tool in the box of many a soaring pilot -- especially the older ones who didn't start out with all the fancy stuff.

JB

 

[Uncayimmy]

Once again, there is nothing in the problem that states you can't use clues outside the cockpit to fly the plane. If you wish to know when you've completed a circle, pick a cloud -- this will give you relative reference for the circle but no information related to steady wind direction.

You still haven't answered my question, but I guess by not saying I am wrong, my explanation must be right: Use the horizon to set your bank angle then pick a fixed reference point to determine when you've completed a circle. Is that how you fly a circle?

Do I have to actually know each time I complete a circle for your answer to work? I think it does, but I may not be understanding. If not, then tell me so I can try to understand the answer better.

If it does matter, then help me out. You said "the ground is featureless and bland -- you can derive no directional information from it." Okay, but you say I can use a cloud bank as my reference point to know that I have completed a circle. Like I said, I don't fly, so how reliable is this?

Is there a way of knowing it's inside the moving air mass and that it is moving as the whole air mass moves? I've watched clouds overhead move at different rates essentially "straight up" from where I was standing.

Does the cloud bank have to be inside the air mass to be able to accurately determine a circle?

 

[Clive]

As someone with something around 3,000hrs in hang gliders, most of those with no instruments whatsoever, the brain alone is plenty instrument enough.

Just curious, what sort of techniques can you use to judge whether you're climbing or descending when you've got no instruments at all (apart from brain!), and the ground/terrain etc., doesn't provide obvious clues to easily allow vertical movement to be determined - perhaps something like a relatively close hilltop apparently dropping below something further away as you climb, etc.? (Can that be called "parallax"?)

Anyway, I haven't done any real "brain alone" soaring so I don't really know anything about that. I imagine that sometimes you might be in a stable glide through air that perhaps you can reasonably assume to not be moving vertically in any significant way. Then you might feel increased turbulence and a temporary sensation of upwards acceleration as you enter a region of rising air and vice versa when you exit the thermal? But is there always a clear-cut transition of that kind to give it away? Couldn't you get some thermals where the transition is fairly smooth and gradual and you also don't have any other other reliable visual cues? In that case I can't really see how you could get away from needing some instruments to help you out.

Note also, my comments about minimal instruments (plus brain) were meant to be interpreted in a context where you're flying on instruments alone, with nothing useful whatsoever to be seen outside. Obviously if you can see the horizon, and feel the "wind" on your face, then you don't need my airspeed indicator and artificial horizon or similar. But judging relatively fine vertical movement when you are fairly high above the ground sounds like a trickier problem to me. (Then again, I have precisely zero hours of hang glider time - or maybe I can claim a few seconds if you count running along the ground just to get the feel of one!)

 

[Clive]

How do you fly in a circle without using clues outside of the cockpit?

Let me have a shot at this. You do need to have some information. Basically the "easy way" to fly in a circle is to maintain a constant airspeed, angle of bank, and angle of attack. In this puzzle, you could achieve that (and also maintain your altitude) in a glider of some kind if you are in a thermal. Once you've established your aircraft in the correct configuration, then your wing is producing a fixed amount of lift, and as you're also at some constant angle of bank that means your lift vector is tilted to the side, giving you a constant force towards the center of your orbit. That gives you the constant centripetal force required to move in a circular path.

Of course, outside of a thermal you could do the same thing in your unpowered aircraft also, but you'd also have to be descending (relative to the ground). So the perfect circle (from above) is actually a spiral when viewed in 3D.

JB allowed us to see the horizon (to get angle of bank for example). Alternatively you'd need to have some instruments in the cockpit and then not need to look out at all (in theory). You don't absolutely need an artificial horizon in the cockpit if you were flying on instruments alone, but it would sure make things easier!

 

[Uncayimmy]

JB allowed us to see the horizon (to get angle of bank for example). Alternatively you'd need to have some instruments in the cockpit and then not need to look out at all (in theory). You don't absolutely need an artificial horizon in the cockpit if you were flying on instruments alone, but it would sure make things easier!

Thanks, Clive. Can you address my other post as well about whether knowing you've completed a circle is a requirement or not?

 

[ThinAirDesigns]

You still haven't answered my question, but I guess by not saying I am wrong, my explanation must be right: Use the horizon to set your bank angle then pick a fixed reference point to determine when you've completed a circle. Is that how you fly a circle?

I guess I have to say I still don't fully understand why you ask this question ... seems a little silly for you to ask how to make as circle in *any* craft, land, water or air. But here it is ... turn left or right until you're pointed back where you started. There, happy now?

Do I have to actually know each time I complete a circle for your answer to work? I think it does, but I may not be understanding. If not, then tell me so I can try to understand the answer better.

Roughly, yes. Perfectly, no.

Okay, but you say I can use a cloud bank as my reference point to know that I have completed a circle. Like I said, I don't fly, so how reliable is this?

Definitely reliable enough. Depending on time of day, my most common reference is the sun. Since thermal soaring conditions most often includes cloud conditions, they are my second most common reference. There's no question that a significant portion of the time I am also able to use a point the ground near the horizon -- say a distant peak.

Is there a way of knowing it's inside the moving air mass and that it is moving as the whole air mass moves? I've watched clouds overhead move at different rates essentially "straight up" from where I was standing.

Does the cloud bank have to be inside the air mass to be able to accurately determine a circle?

In the few seconds it take to complete a circle, coupled with the rather rough level of accuracy needed, I have never had to worry about whether a cloud was or was not in the same airmass with me to utilize this method.

You will encounter more variations *within* the thermal than the external variations you are concerned with.

JB

 

[ThinAirDesigns]

Just curious, what sort of techniques can you use to judge whether you're climbing or descending when you've got no instruments at all (apart from brain!), and the ground/terrain etc., doesn't provide obvious clues to easily allow vertical movement to be determined - perhaps something like a relatively close hilltop apparently dropping below something further away as you climb, etc.? (Can that be called "parallax"?)

Well, it's a combination of internal accelerometer and the age old soaring adage "when you're down, fly the ground -- when you're high, fly the sky". Pretty much that means if you're low you can get clues from the ground and when you're high you get your clues from the clouds.

Thermal lift tends to be quite focused and one learns over time to fairly clearly identify the way the edge of a thermal feels through the wing. By probing the edges and listening to your internal accelerometer you can get pretty damn good at climbing. I use visual clues more as an 'averager' to my seat of the pants instant sense.

The part that is far harder without a vertical speed instrument is cruising between thermals. While lift is focused, sink (which of course is inbetween the lift) tends to be much more broad and smooth. Since the stronger the sink the faster one needs to fly to optimize glide path, it's pretty important to know the velocity of the sink -- and with it's broad nature I find it tough.

Probably 95% of the time I can climb equally well with or without instruments. For obvious reasons, the exceptions would definitely be very light, smooth lift far from visual clues. Gliding accurately I'm nowhere near that good.

I love soaring because of it's quiet, natural feel and I enjoy instrument free flying as it adds to the challenge and doesn't disturb the part I love.

JB

 

[Uncayimmy]

I guess I have to say I still don't fully understand why you ask this question ... seems a little silly for you to ask how to make as circle in *any* craft, land, water or air. But here it is ... turn left or right until you're pointed back where you started. There, happy now?

Why are you getting snippy? I asked a simple question. I told you I don't fly, so I'm choosing not to make assumptions. As Clive generously pointed out, simply turning left without regards to altitude will cause you to fly in a spiral rather than in what I consider a circle, though I wouldn't argue with anybody who wanted to call it a circle.

My original train of thought was simply trying to figure out the difference between using external clues to fly and using external clues to figure out the wind direction. Understanding how a circle is executed was part of that.

As originally written it sounded like a windowless cockpit, which is why I was going that direction to begin with.

Definitely reliable enough. Depending on time of day, my most common reference is the sun. Since thermal soaring conditions most often includes cloud conditions, they are my second most common reference. There's no question that a significant portion of the time I am also able to use a point the ground near the horizon -- say a distant peak.

I figured you could use something on the ground, which is why you excluded it. I did not consider the sun. I dismissed clouds as not being reliable enough.

In the few seconds it take to complete a circle, coupled with the rather rough level of accuracy needed, I have never had to worry about whether a cloud was or was not in the same airmass with me to utilize this method.

As a non-pilot, I figured it took a lot longer than a few seconds to fly in a circle. This is why I ask questions. You learn something new every day.

With all that said, could I have lined up the sun on or more points on the cockpit (put a fingerprint on the glass, for example), then determine based on the actions used to keep it there how the air mass was drifting?

 

[Clive]

Thanks for your reply JB.

When reading your puzzle description I think perhaps a few of us (but definitely me!) assumed more than you meant by the statement about not being able to use things outside for clues. For me, that and the later thing you said about the ground being bland and featureless (or something to that effect) made me think the idea was to imagine also that there were no clouds and so on even though you didn't explicitly say that. I.e. Everything is kind of uniform in every direction - and perhaps the sun is directly overhead also - whereas it now seems more likely that you really only meant there was nothing really visible outside to directly give away the wind direction but that the world was more or less normal in all other ways.

Perhaps UncaYimmy was also thinking along these lines, as if you take the featureless bland landscape (and no clouds, etc.) idea too far you also don't have any reference points to determine when you've completed an orbit or are only halfway round, etc, (although I'd mentally skipped past this "difficulty" by allowing myself have a compass, or deciding that my internal clock and superior knowledge of my aircraft's normal performance would be enough to judge things like that even without external references).

Anyway, just thought I'd mention this in case you pose this puzzle again somewhere else later on. A little more detail about that area might save your next victims from tying themselves in knots trying to get around additional difficulties that you didn't intend to put in there!

ETA: I wrote and posted this before noticing that UncaYimmy had replied already.

 

[ThinAirDesigns]

Why are you getting snippy?

Because I believe you're reason for asking the question is different than you wish to imply.

I asked a simple question.

And again, unless you're asking about the technical bits of a aircraft turn -- aileron/rudder/elevator coordination( which you don't seem to be) it just doesn't make sense to me. If you consider "turn left until you're pointed back the way you started" an answer, it's not much of a question -- if you want the moment by moment details of how the controls operate, I'm happy to answer that but it's not relevent to the problem.

As a non-pilot, I figured it took a lot longer than a few seconds to fly in a circle.

Thermals tend to get stronger in their core (center). The tighter the circle you make, the stronger lift you are in. This velocity increase from the thermal is offset by the fact that the higher the bank angle (how much your wings are tilted) the higher your sink rate. This means that for best climbing performance the aircraft should be level but to stay in the strongest part of the thermal you need to be banked very steeply. By practice you learn how steep to bank to get the best overall performance (this angle varies with thermals strength and aircraft performance of course). Often times in my hang glider that is around 45degrees, perhaps 150 to 200 ft in diameter and maybe 6rpm.

With all that said, could I have lined up the sun on or more points on the cockpit (put a fingerprint on the glass, for example), then determine based on the actions used to keep it there how the air mass was drifting?

You can't get any useful drift information from the sun with the naked eye. Just take a mental snapshot of the sun's relation to you and then blindfold yourself and have someone drive you a half a mile and try again. Can you tell if you were moved N/S/E/W from now glancing at the sun?

JB